Abstract

Starting from the equation of motion in the density matrix formulation, we reformulate the analytical gradient of the excited-stateenergy at the time-dependent density functional theory level in the nonorthogonal Gaussian atom-centered orbital (AO) basis. Analogous to the analytical first derivative in molecular-orbital (MO) basis, a Z-vector equation has been derived with respect to the reduced one-electronic density matrix in AO basis, which provides a potential possibility to exploit quantum locality of the density matrix and avoids the matrix transformation between the AO and the MO basis. Numerical tests are finished for the excited-state geometry optimization and adiabatic excitation energy calculation of a series of small molecules. The results demonstrate the computational efficiency and accuracy of the current AO-based energy gradient expression in comparison with the MO-based scheme.

Received 14 September 2010Accepted 06 January 2011Published online 26 January 2011

Acknowledgments:

Financial supports from National Science Foundation of China (Grant Nos. 20833003 and 21073168), the National Basic Research Program of China (Grant No. 2011CB808501) and Chinese Academy of Science are acknowledged.